Nominal Signal Deformations: Limits on GPS Range Accuracy

Presented at GNSS 2004 The 2004 International Symposium on GNSS/GPS

Sydney, Australia 6?8 December 2004

Nominal Signal Deformations: Limits on GPS Range Accuracy

R. E. Phelts

Stanford University, Department of Aeronautics and Astronautics

Durand Bldg., Room 060 Stanford California 94305 Tel: (650) 724-7139 Fax: (650) 725-5517 Email: pheltsre@stanford.edu

D. M. Akos

University of Colorado 101 ECAE ? Aerospace Engineering Sciences

429 UCB Boulder, CO Tel: (303) 735-2187 Fax: (303) 492-7881 Email:dma@colorado.edu

Presenter Name(s)

R. Eric Phelts

ABSTRACT

Satellite-based navigation requires precise knowledge of the structure of the transmitted signals. For GPS, accurate knowledge of the shape of the ranging codes is required to ensure no biases are introduced into the position solution. It is generally presumed that all GPS-like satellite signals were virtually identical, however new research has shown that there may be significant variations between different GPS satellite signals. Since most GPS receivers require signals from four or more satellites, many GPS navigation solutions (past, present, and future) may contain unexplained bias errors ranging from a few centimeters to several meters.

Current GPS receivers presume GPS signals are identical and that range errors result solely from atmospheric effects, clock errors and multipath. In fact, this type of error, if present, is likely often mistaken for multipath. However, a separate error may result from non-uniform signal distortion between GPS signals. This error is believed to result from small filter group delay variations between satellite transmission antennas. Accordingly, ranging accuracy may more-heavily depend on factors such as receiver front-end filtering and correlator spacing.

This paper presents high-resolution, low-noise measurements to directly compare the received signals from various satellites. It is shown that GPS signals may differ significantly from one to another. Also, it proposes that ranging accuracy may have fundamental limitations not related to the usual

random, noise-like error sources discussed in previous papers. Further, it is concluded that high-integrity augmentation systems such as WAAS and LAAS--which attempt to protect wide range of receiver types--may need to take additional steps to limit the impact of these errors on aviation users.

KEYWORDS: signal, deformation, distortion, filters, group delay, GEO, bias, nominal, correlation peak, range error

1. INTRODUCTION

It is well-known that signal distortions or deformations cause range errors. Many have been studied and analyzed by many in the past. Multipath is a form of signal deformation that acts similar to the effects discussed in this paper. Its effect on GPS ranging capability has been extensively analyzed for many years. Signal deformations caused by satellite failures are somewhat less well-known; however these too have been analyzed and quantified in the past. (Phelts et al. 2000; Macabiau and Chatre 2000; Edgar et al, 2000).

The effects of nominal signal distortions on ranging performance have much more recently become of interest to the navigation community. The Wide Area Augmentation System (WAAS) employs geostationary satellites (GEOs) for datalink and ranging purposes that have significantly different filter characteristics than GPS satellites. This difference, along with filter and tracking disparities between the reference and user receivers have been found to lead to potentially significant range biases (Phelts et al, 2004). The Local Area Augmentation System (LAAS) does not rely on GEO measurements. Still, its more-stringent range accuracy requirements make the results of this type of analysis extremely pertinent for navigation using GPS satellites alone.

In practice, it is quite challenging to both observe and identify biases from nominal signal deformations. Position errors, range errors and correlation peak distortions are their effects. Position domain measurements are easiest to obtain and to process; correlation peak measurements are perhaps the most difficult. Despite this, these kinds of biases are mostdifficult to observe in the position domain and are least hidden in the correlation domain.

In the position domain, its effects are very similar to slowly-varying multipath. The number of satellites tracked and their varying geometries generally cause the position error biases to slowly vary with time. And, since multipath (and any residual atmospheric error) is always present to some degree on each code range measurement, some of the errors attributed to multipath, may actually be due to these nominal biases. In the range domain, errors from nominal biases are virtually indistinguishable from static multipath. Special measures must be taken (e.g., using a high-gain, directional antenna) to identify them. The directional antenna, of course, then limits the number of space vehicles (SVs) that can be observed at any given time. Correlation domain techniques--the approach taken in this paper--require morespecialized receiver hardware in addition to the antenna requirements; however, they provide the most flexible means of observing the biases.

This paper uses methods and tools developed for GEO bias determination and satellite signal deformations to uncover the nominal distortions present on GPS satellites. Some of this work has been done by Mitelman (2005) and is briefly summarized in Section 2.4.1. As employed by Mitelman (2005), the work here also combines high-gain antenna measurements with a high-resolution signal analyzer and a software radio receiver. Additionally, this analysis takes

a comprehensive look at the output several of the GPS satellites though the use of correlation peak comparisons--measurements that directly translate to user ranging performance. This paper quantitatively compares the ranging performance of these satellites to ideal, theoretical predications and to each other.

2. CODE CORRELATION AND GPS ERROR SOURCES

The autocorrelation of ideal C/A pseudorandom noise (PRN) codes form perfect, triangular correlation peaks. For the current GPS constellation (consisting of 32 distinct PRNs) and the current two Inmarsat GEO PRNs, the slopes of those peaks may have three nominal values (Phelts, 2001). However, the peaks are perfectly symmetric and are effectively identical from SV-to-SV. (The slopes of the correlation peaks need not be identical from PRN-to-PRN, or rather SV-to-SV. Provided the correlation peaks are symmetric, the discriminator curves will share a common zero-crossing.) Traditional analyses presume this is the correct model for the satellite signal as transmitted by GPS satellites.

Throughout this paper, range errors will be discussed in terms of their effect on the correlation peak. GNSS error sources affect correlation peaks in different ways. Some produce position errors, others do not; they may produce timing errors instead. Some are present all of the time and others vary with time and still others only occur under failure conditions. The subsections below briefly describe many of these and their affect on correlation peaks.

2.1 Atmospheric Errors

The ionosphere and troposphere cause ranging biases. They effectively cause a shift in the correlation peak that is not accompanied by asymmetry. Higher-order effects of the ionosphere may cause negligible correlation peak distortion.

2.2 Timing Errors

Timing errors exist nominally due to the nature of most (imprecise) receiver clocks, which must be calibrated using GPS. In addition to this, however, residual errors in the satellite clock may exist. Also, the satellite clock may fail and cause a particular range solution to drift off until the problem is corrected by the Ground Control Segment. These effects cause range biases that manifest themselves as shifts in the correlation peak; they do not cause correlation peak distortion. If the error is in the receiver clock, the result is an effective uniform shift of all received signals or correlation peaks that does not lead to range or position errors.

2.3 Receiver Filtering

If the satellite signals are effectively matched from SV-to-SV, any filtering performed by the front ends of GPS receivers will affect all incoming signals identically. Since front end filters, in general, do not have perfectly linear phase, they do create some amount of correlation peak asymmetry. Still, provided all receiver correlator spacings are identical in a given receiver, this will translate into a uniform bias, or correlation peak shift, across all range

measurements. This bias will be solved for in the navigation solution and will not affect code positioning accuracy. If, however, the satellite signals are not identical from SV-to-SV, range errors may exist and adversely affect the navigation solution. This latter case is discussed further in the next subsection.

2.4 Signal deformations

For the purposes of this paper, signal deformations are defined as distortions of the signal that cause the peak itself to become, in general, asymmetric. These may result from either thermal noise, multipath, satellite failures or filter effects (e.g., filter group delay response) or some combination thereof. Whenever these distortions occur, they are generally not identical on all incident signals. Unpredictable range errors are often the result.

Multipath and thermal noise, of course, are always present to some extent. Satellite failures, such as the type that affected SV19 in 1993, are rarer (Edgar et al, 2000). These have since been modeled as in Figure 1 (Phelts et al, 2000). Filter distortions generally occur due to the presence of analog components in the signal chain. They are caused by group delay variations (i.e., non-linear phase) across the passband of a given filter. The filters may be those on the transmission path of the satellite signal or in the front end of the receiver. This too leads to range biases that affect identical signals the same. However, if the satellite transmission path filters are not identical they will cause the respective signals to differ. If the signals differ, then the receiver filter will accordingly modify them in slightly different ways.

C/A PRN Codes

2.5 2

digital

1.5

1

0.5

0

-0.5

-1

-1.5

-2

-2.5

0

1

2

3

4

5

6

2.5 2

1.5

analog

1

0.5

0

-0.5

-1

-1.5

1/f -2

-2.5

d

0

1

2

3

4

5

6

2.5 2

1.5 1

0.5 0

-0.5 -1

-1.5 -2

-2.5 0

1/fd

1

combination

2

3

4

5

6

Chips

1 0.8 0.6 0.4 0.2

0 -1.5

1 0.8 0.6 0.4 0.2

0 -1.5

Correlation Peaks

Dead zones

-1

-0.5

0

0.5

1

1.5

Distortions

-1

-0.5

0

0.5

1

1.5

1 0.8 0.6 0.4 0.2

0 -1.5

False Peaks

-1

-0.5

0

0.5

1

1.5

Code Offset (chips)

Figure 1. A depiction of the accepted code and correlation models for satellite signal deformation failures. More details on this model are provided by Phelts (2001).

The WAAS GEO signal is a notable example of the result of a filter-induced, nominal signal deformation. The current WAAS geostationary satellites broadcast narrowband (2.2MHz) ranging signals. The filters on the GEO signal path have characteristics which differ significantly from that of the GPS signals. The transmitted signals are deformed differently than are GPS signals; a given receiver processes them slightly differently. Substantial range biases may result if proper mitigation measures are not taken (Phelts et al, 2004).

2.4.1 PRN Code Domain Observations

The raw GPS PRN codes themselves, as generated, are not ideal. If the rise and fall times of the chip transitions are not matched, an ideal correlation peak may develop a small "dead zone" distortion. This type of distortion is illustrated in the first plot of Figure 1. This effect and the measurement techniques used to precisely measure the raw PRN codes are more completely described by Mitelman (2005). The extent of this asymmetry is summarized for several GPS PRNs in Figure 2.

Estimated (ns)

Estimates of C/A code Sorted by SV Block Type (II, IIA, IIR)

5.5

5 Block II

Block IIA

Block IIR

4.5

~4.5ns on

PRN14

4

3.5

3

2.5

Up to 10ns of modeled digital

2

distortion yields:

1.5

< 6cm of differential range

error

1

< 1.6m of SPS range error

0.5

30.22 17.92 1117.2 1155.2 1293.2 2235.2 2277.2 3011.2 3252.2 3391.2 4039.2 4073.2 5113.2 5151.2 2509.2 6238.2 6174.2 7118.2 7156.2 PRN (In chronological order of launch date, within each group, oldest to newest)

Figure 2. High-resolution measurements of lead/lag (digital) code distortion on several GPS PRNs (Mitelman, 2005).

Two key observations in Figure 2 should be noted. First, none of the PRN codes have a digital distortion equal to zero; none of the broadcast codes are ideal. Second, the largest deformation of this type was approximately 4.5ns and was observed on PRN 14. PRN14 is broadcast on SV14--a relatively new, Block IIR SV. Ironically, the older SVs have relatively smaller, but still non-zero, digital distortion (1-2ns). Figure 2 confirms that modeling the GPS ranging signals as ideal PRN codes is not precisely correct. Still, it does not provide insight into other types of deformation (e.g., analog or filter-induced distortions) that may be present on the signals.

Note that the position errors one might expect due to these nominal deformations will vary depending on the specific satellites included in a given navigation solution. However, if the code asymmetry is as large as 10ns on a single SV ranging signal, and all others are ideal and have no lead/lag distortion--as assumed by Phelts, et al (2000) and by Macabiau and Chatre (2000) for traditional signal quality monitoring (SQM) analysis--the SPS range errors may be as large as 1.6 meters. For differential users, such as those who use the Local Area Augmentation System, the errors may be as large as 6cm. (The details of this particular SQM analysis are beyond the scope of this paper.)

2.4.1 Correlation Domain Observations

Differences in correlation peak measurements can easily be verified with a more-conventional GPS receiver-antenna setup (Brenner et al, 2002). Figure 3 shows an overlay of eight

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